Question

if ∆ABC~∆DEF and A=45 E=87° then find C

Answer 1

Answer:

Step-by-step explanation:

Angle A = angle D= 45°

Angle B = angle E= 87°

Angle C = angle F

BY ANGLE SUM PROPERTY IN TRIANGLE ABC

ANGLE A +ANGLE B+ ANGLE C= 180°

45°+87°+ANGLE C=180°

ANGLE C= 48°

Answer 2

The measure of ∠C is 48° .

Step-by-step explanation:

It is given that ∆ABC≅∆DEF.

Thus, the two triangles are congruent triangles. It means the corresponding parts of both the triangles will be equal.

• side AB = side DE,
• side BC = side EF, and
• side AC = side DF.
• ∠A = ∠D,
• ∠B = ∠E, and
• ∠C = ∠F

The measurements of two angles are given as:

• ∠A = 45° ⇒ ∠D = 45°
• ∠E = 87° ⇒ ∠B = 87°

Now, in ∆ABC,

∠A + ∠B + ∠C = 180° ( Angle sum property of a triangle).

Substituting the values of the angles A and B in the above equation, we get,

45° + 87° + ∠C = 180°

∠C = 180° - 45° - 87° = 180° -132° = 48°

Hence, ∠C = 48°.